Download + v if

Detector Input Impedance
Consider an idealized, lossless detector, driven by an unmodulated carrier:
1:a
+
+
avif (0-pk)
vif (0-pk)
_
RIN 
RL
_
RL
2a 2
RDET
IF (0  P )

+
PL
avif (DC)
2
2
v
IF  RMS 
2
a
RL
_
RL

2
av


2

RL
2
vIF
 RMS 
R
L
2a
2

 PIF
Minimum Power to the Detector
For a modulated signal, the the minimum peak AC voltage into the detector
must exceed the diode turn-on voltage. If the carrier voltage coming out of
the final IF amplifier is EC(0-pk), then aEC(1-m) > VD ; or
EC 
VD
a 1  m) 
The minimum carrier power required is
2
 VD



2
a
1

m

  VD2 1
EC (min)

PC (min) 


2 RIN
RL 1  m 2
 RL 
2 2 
 2a 
The minimum total power into the detector must be:
2
V
PDET (min)  PC (min) 1  m2 2   D
RL
1  m 2 2 

2 
 1  m  
Note that the
minimum total
power required for
undistorted output
is not affected by
the transformer
turns ratio!
Minimum Receiver Gain
In terms of sideband power,

PIF (min) VD2 
1  m2 2


PSB , DET (min) 

2
2
2
 2 m  1 RL   2 m  1 1  m  
VD2

RL
 m2 2  V 2  m 2 V 2  1 2
D
 D 



 
2
2
R
1

m
2
R
1
m

1


1

m
 
 

L
L 
The receiver should have sufficient total gain (GT) such that the signal out of the
final IF amp will be sufficient to drive the detector without distortion whenever
the signal level entering the antenna has sufficient power to make the detector
output exceed the minimum required output SNR (12 dB for voice
communication). This occurs when the sideband power entering the antenna is:
PSB , ANT (dBW )  kT0 B(dBW )  NF (dB)  SNRMIN (dB)
Minimum Receiver Gain (cont)
Expressing PSB,DET in dB, we have:
 VD 2 
PSB, DET  dBW   10log 
  20log 1 m  1
 2 RL 
Note that the first term on the RHS only reflects detector parameters,
and the second term reflects only modulation index. It is convenient to
refer to the first term as “Reference Detector Power”, PDR(dBW), as it
captures the two important detector parameters in one number.
The minimum required total gain for the receiver is:
GT (dB)  PSB , DET (dBW )  PSB , ANT (dBW )
Receiver Sensitivity
Receiver Sensitivity is a key specification which defines the minimum
signal level required at the receiver input to produce a specified SNR at the
detector (demodulator) output.
It is usually expressed in dBf (femto-watts) or microvolts (RMS, 50 ohm
source) .
We have already determined the minimum sideband power required at the
receiver input to produce a specified SNR , so total power required would be:
PSEN W   PSB , ANT W   2 m 2  1
PSEN  dBf   PSB , ANT  dBW   10 log  2 m 2  1  150dB
VSEN VRMS  
PSEN W   50
VSEN  VRMS   VSEN VRMS  106
Example
Example: An AM (m = 0.6) receiver has the following characteristics:
Detector RL = 5000 
Detector VD = 0.2 V
B = 20 kHz
NF = 15 dB
10 log10  2 m 2  1  8dB
20 log10 1 m  1  3.5dB
Threshold SNR = 12 dB
RF
Front End
kT0 B  161dBW
IF Strip
SNR = 12 dB
@ PANT = PSEN
Detector
PSB,ANT
VD2  0.2 
PDR 

 4W  54dBW
2 RL 2  5K
2
PSENS  dBW    161dBW  15dB  12dB   8dB
 126dBW
 24dBf  0.25 pW
PSB , DET  dBW   PDR (dBW )   3.5dB 
 50.5dBW
VSENS  0.25 pW  50  3.5V
GT  dB  PSB, DET  PSB, ANT  50.5dBW   143dBW   92.5dB
Dynamic Range
From an AC Load Line Analysis, we can determine the
maximum 0-Pk amplitude of vIF < VIF(max).
If we are dealing with a modulated AM signal, the maximum
0-Pk amplitude of vIF is EC(1+m) < VIF(max).
We have previously determined that to avoid negative peak
clipping, the minimum 0-Pk AC voltage into the detector
must exceed the diode turn-on voltage: aEC(1-m) > VD .
VIF  max 
VD
 EC 
a 1  m 
1  m 
Dynamic Range
The ratio of maximum to minimum signal range for undistorted
output is called “Dynamic Range”. Expressed in dB it is:
  VIF (max)   1  m  
 EC (max) 
20 log10 

  20 log10 a 

E
(min)
V
1

m

D

 C

 
Example: The final amplifier in the IF strip of our previous receiver will
accommodate a maximum AC output of 6 volts 0-pk, and has an output impedance
of 100 ohms.
Since RDET = RL/2 = 2500 , the transformer should have a = 5 to match the IF
amp to the detector.
For modulation index m = 0.6, the dynamic range is:
  6  1  0.6  
20log10 5 

   15.7dB
  0.2  1  0.6  
Automatic Gain Control
The previous example uses reasonable numbers, and the result, 15.7 dB, is
not a respectable value for dynamic range. If the radio’s maximum range is
50 miles, then the IF will clip at ranges less than 1.5 miles, and this would be
unacceptable.
The solution is to provide a means for reducing the gain of the receiver when
the output signal begins to approach the clipping range.
Since the detector output contains a DC level proportional to the received
carrier level, this DC level can be extracted from the detector output using a
low-pass filter, and fed back as a control voltage to reduce receiver gain.